Symmetric alcoved polytopes
type: Item
instance of: scholarly article
title: Symmetric alcoved polytopes
zbMATH Open document ID: 1302.52014
author: Annette Werner
author: Josephine Yu
published in: The Electronic Journal of Combinatorics
publication date: 2014-09-04T00:00:00Z
full work available at URL: https://arxiv.org/abs/1201.4378
full work available at URL: v21i1p20
review text: Summary: Generalized alcoved polytopes are polytopes whose facet normals are roots in a given root system. We call a set of points in an alcoved polytope a generating set if there does not exist a strictly smaller alcoved polytope containing it. The type \(A\) alcoved polytopes are precisely the tropical polytopes that are also convex in the usual sense. In this case the tropical generators form a generating set. We show that for any root system other than \(F_4\), every alcoved polytope invariant under the natural Weyl group action has a generating set of cardinality equal to the Coxeter number of the root system.
Mathematics Subject Classification ID: 52B15
Mathematics Subject Classification ID: 14T05
Mathematics Subject Classification ID: 17B22
zbMATH DE Number: 6340118
zbMATH Keywords: polytopes
zbMATH Keywords: root systems
zbMATH Keywords: tropical geometry
MaRDI profile type: Publication
arXiv ID: 1201.4378
cites work: \(Y\)-systems and generalized associahedra
cites work: Tropical and ordinary convexity combined
cites work: Lattice polytopes cut out by root systems and the Koszul property
description: scientific article; zbMATH DE number 6340118